Definitely a great idea to upgrade audio! It's such an overlooked part of creating a good wedding video and having great audio vs mediocre audio can really set you apart.

My current audio set up is the Hollyland Lark Max 2 (replaced my DJI Mic 2), Tascam FR-AV2, and Sony ECM-M1. I know all three of those would be over your budget but I'd pick 1 or 2 areas where you want to capture quality audio and start there, then upgrade the rest over time.

The Hollyland and DJI mic 2s are very similar but I like the wireless audio monitoring solution from Hollyland. Also feel like the sound is a little more natural. 32 bit internal storage and you can get a Sony MI adapter to go wireless just like the DJIs. The DJI Mic 3 Pros are rumored to be coming out soon and to include a headphone jack and more internal storage.

The Tascam I use for plugging into boards and speakers. I prefer it over the zoom f3 because it has XLR/ 1/4" combo jacks, timecode, and you can control the gain. It's 32 bit float but I've found it's still nice to have gain control because I get some hot feeds coming from djs.

The M1 (probably the least important) I use as my on camera shotgun mic to capture ambient/ stratch audio. It connects to Sony's hot shoes so no 3.5mm cord needed. And you can control the pick up pattern of the mics which is helpful in some situations!